To express the measurement of 43,700 cm in scientific notation, follow these steps:
1. Identify the significant figures in the distance. Here, the number 43,700 has four significant figures: 4, 3, 7, and 0.
2. Rewrite the number such that it lies between 1 and 10 by placing the decimal point after the first significant figure:
[tex]\[
4.3700
\][/tex]
3. Count how many places the decimal point has moved from its original position to its new position. In this case, the decimal point moves 4 places to the left:
[tex]\[
43700 \rightarrow 4.3700
\][/tex]
4. Express the original number as a product of this rewritten number and a power of 10. Since we moved the decimal point 4 places to the left, we multiply by [tex]\(10^4\)[/tex]:
[tex]\[
4.37 \times 10^4
\][/tex]
After following these steps, the measurement 43,700 cm can be written in scientific notation as:
[tex]\[
4.37 \times 10^4 \, \text{cm}
\][/tex]
Therefore, the correct choice is:
C. [tex]\(4.37 \times 10^4 \, \text{cm}\)[/tex]
